Linearity and loopholes: On Bell inequalities and measurement-based quantum computation

We show [1] that multi-party generalisations of the CHSH inequality can be elegantly derived in a framework similar to measurement-based quantum computation. This gives an operational meaning of what it means to violate a CHSH-type inequality, which allows us to characterise the effect of "loopholes" in Bell inequality experiments. We show that adaptive measurements of the kind which occur in measurement-based quantum computation may be simulated without introducing a loophole, and that this means that one can contrast local hidden variable correlations with a wider class of quantum correlations than traditionally considered.